Question

The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

Answer 1

Yes, this is a typical pythagorean triad.

Since the theorem is: $c^{2} = a^{2} + b^{2}$
And by inspection, $5^{2}$ would be the hypotenuse,
$5^{2} = 3^{2} + 4^{2}$
25 = 9 + 16
RHS = 9 + 16 = 25 = LHS
Therefore, we have proved that the values fit into pythagoras' theorem, which means that the triangle is a right triangle (that is the central idea of this theorem).